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A numerical algorithm for the involutory schrödinger type problem
(Maltepe Üniversitesi, 2019) Ashyralyev, Allaberen; Abbas, Twana
It is known that various problems in physics lead to the Schr¨odinger equation. Methods of solutions of the problems for Schr¨odinger equation have been studied extensively by many researchers (see, e.g., [1, 2, 3, 4], and the references given therein). In this study, applying Fourier series, Laplace and Fourier transform methods, we can obtain the solution of several Schr¨odinger type involutory problem. The first and second order of accuracy difference schemes for the numerical solution of the initial boundary value problem for one dimensional Schr¨odinger type involutory equation are presented. Numerical results are given.
On the boundedness of the Schrödinger type differential equation with time involution
(Maltepe Üniversitesi, 2021) Ashyralyev, Allaberen; Abbas, Twana
. In the present paper, the initial value problem for the Schrodinger ¨ type involutory partial differential equation is studied. Applying Green’s function of space operator, we get formula for solution of this problem. In applications, the theorem on stability of this problem is established. Furthermore, this formula is applied to the existence and uniqueness of bounded solution of nonlinear problem with involution.